This exercise uses the population growth model. A certain culture of the bacte

Algebra
Tutor: None Selected Time limit: 1 Day

This exercise uses the population growth model. 

A certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to double every 1.5 hours.
Streptococcus A
(12,000 × magnification)
(a) Find an exponential model 
n(t) = n02t/a
 for the number of bacteria in the culture after t hours. 
n(t) = 
 

(b) Estimate the number of bacteria after 20 hours. (Round your answer to the nearest whole number.) 
 bacteria 

(c) When will the bacteria count reach 10,000? (Round your answer to one decimal place.) 

t =  h

Jul 15th, 2015

Thank you for the opportunity to help you with your question!

1)     n(t) =n0 2^t/a

   n(1.5)=n0 2^1.5/a

   2n0 =n02^1.5/a

   2=2^1.5/a

 a=1.5

so the equation becomes

n(t) =n0 2^t/1.5




2)so after t=20

n(20)=8*2^(20/1.5)

         =82570



3)10000=8*2^(t/1.5)

log1250=t/1.5 log2

t=15.42

  

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 15th, 2015

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